Conventional xe2x80x9ctrue-amplitude migrationxe2x80x9d is a form of migration of the Kirchhoff type using a weighted diffraction stack. This technique has become increasingly popular as a seismic tool for quantitative discrimination of lithology and fluids in hydrocarbon reservoirs. However, the term xe2x80x9ctrue amplitude migrationxe2x80x9d is to some extent misdescriptive. From a physical viewpoint, valid amplitude information may only be preserved if the entire processing line is designed for that purpose. In most cases, it is not. Thus, it is virtually impossible to have a xe2x80x9crealxe2x80x9d true amplitude migration in practice, because many processing procedures affect the amplitude preservation.
Furthermore, conventional true amplitude weight terms are complicated and do not consider many necessary factors. In a smoothly varying velocity field, for example, the amplitude weight depends on the travel-time, amplitude, ray-tube spreading factor, and takeoff angles in the shot and receiver points.
Even further, conventional approximations of the reflection travel-times often assume a small offset-to-depth ratio, and their accuracy decreases with increasing offset-to-depth ratio. Hence, they are not suitable for migration of long-offset reflection seismic data.
Finally, conventional Kirchhoff time migration for transversely isotropic media with a vertical symmetry axis (VTI media) is implemented using an offset-midpoint travel-time equation. However, travel-times as functions of offset and common midpoint (CMP) are given by the simple analytical double-square-root equation (DSR) designed for homogeneous media. This travel time is not well suited for inhomogeneous media.
Thus, there is a long felt need for a relative true amplitude migration process which preserves relative amplitude, considers the appropriate factors, is accurate for long-offset data, and is suitable for vertically transversely isoropic (VTI) media, also called transverse isotropy with a vertical symmetry axis. The present invention addresses the above mentioned concerns.
One aspect of the invention is a method for migrating seismic data. A method according to this aspect of the invention includes selecting an image point, and generating a model of seismic velocity with respect to time. The model includes substantially horizontal layers each having a selected velocity and a selected thickness. A two-way travel time of seismic energy is determined from at least one seismic energy source position to at least one seismic receiver position wherein the seismic energy is reflected from the image point. A ray path is estimated from the at least one seismic source position to the image point and from the image point to the at least one seismic receiver position. The ray path is based on the source position, the receiver position and the velocity model. The two-way travel time of seismic energy through formations to the image point is then determined.